1.4
This presentation is the property of its rightful owner.
Sponsored Links
1 / 7

1.4 PowerPoint PPT Presentation


  • 116 Views
  • Uploaded on
  • Presentation posted in: General

1.4. FORMULAS FOR LINEAR FUNCTIONS. Finding a Formula for a Linear Function from a Table of Data. Example 1 The following table gives data from a linear function for a grapefruit thrown into the air. Find the formula for the function. Solution

Download Presentation

1.4

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


1 4

1.4

FORMULAS FOR LINEAR FUNCTIONS


Finding a formula for a linear function from a table of data

Finding a Formula for a Linear Function from a Table of Data

Example 1

The following table gives data from a linear function for a grapefruit thrown into the air. Find the formula for the function.

Solution

We will look for a function of the form y = mx + b and begin by computing the slope:

Now we can determine b using m and the point (2, 16):

y = -32x+ b; 16 = -32 (2) + b which gives b = 80

So the formula for our function is


1 4

Exercise 26

The following table gives data from a linear function. Find a formula for the function.

Solution

We will look for a function of the form y = mx + b and begin by computing the slope:

Now we can determine b using m and the point (32, 0):

y = 5/9 x + b; 0 = 5/9 (32) + b which gives b = -160/9

So the formula for our function is


Finding a formula for a linear function from a graph

Finding a Formula for a Linear Function from a Graph

Exercise 30

Solution

First we will find the slope of the line using (4, 7) and (12, 3).

We will look for a function of the form y – y0 = m(x – x0) using (4, 7)

y – 7 = – 0.5 (x – 4)

y – 7 = – 0.5x + 2

which simplifies to

y = – 0.5 x + 9

y

The graph gives data from a linear function. Find a formula for the function.

x


Finding a formula for a linear function from a verbal description

Finding a Formula for a Linear Function from a Verbal Description

Example 3

We have $24 to spend on soda and chips for a party. A six-pack of soda costs $3 and a bag of chips costs $2. The number of six-packs we can afford, s, is a function of the number of bags of chips we decide to buy, c.

  • Find an equation relating s and c.

    Solution

  • The amount of money ($) spent on soda will be 3s.

  • The amount of money ($) spent on chips will be 2c.

  • Assuming we spend all $24, the equation becomes:

    2c + 3s = 24

    3s = -2c + 24

    s = – 2/3 c+ 8


Interpreting a formula for a linear function from a verbal description

Interpreting a Formula for a Linear Function from a Verbal Description

Example 3

From (a), the equation is

(b) Graph the equation. Interpret the intercepts and the slope in the

context of the party.

Solution

All soda

No chips

The fact that m = −2/3 means that for each additional bag of chips purchased, we can purchase 2/3 fewer six-packs of soda.

6 packs of soda and 4 bags of chips

All chips

No soda


Alternative forms for the equation of a line

Alternative Forms for the Equation of a Line

  • The slope-interceptform is

    y = mx + b

    where m is the slope and b is the y-intercept.

  • The point-slope form is

    y − y0 = m(x − x0)

    where m is the slope and (x0, y0) is a point on the line.

  • The standard form is

    Ax + By + C = 0

    where A, B, and C are constants.


  • Login